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<p>
<strong>Consultation:</strong>
<br />
Mon 1-2pm Tue 2-3pm Fri 12-1pm in <a href="https://go.unimelb.edu.au/i5cn">Peter Hall</a> 166
<!-- TBA -->
</p>
<p>
<strong>Mailing address:</strong> Alex Ghitza,
<br />
School of Mathematics and Statistics,
<br />
The University of Melbourne,
<br />
Parkville VIC 3010, Australia.
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<h2>About</h2>
<p>
I am an
<a href="https://en.wikipedia.org/wiki/Academic_ranks_(Australia_and_New_Zealand)#Overview_in_Australia">associate professor</a>
in
<a href="https://ms.unimelb.edu.au/research/groups/details?gid=32%22">Pure</a>
<a href="https://ms.unimelb.edu.au">Mathematics</a> at the <a href="https://www.unimelb.edu.au">University of Melbourne</a>, in Australia. My research is in <a href="https://en.wikipedia.org/wiki/Arithmetic_geometry">arithmetic algebraic geometry</a>, an area at the intersection of
<a href="https://en.wikipedia.org/wiki/Number_theory">number theory</a>
and
<a href="https://en.wikipedia.org/wiki/Algebraic_geometry">algebraic geometry</a>. I am also keenly interested in computational aspects of both number theory and algebraic geometry.
</p>
<p>
I am part of the
<a href="https://numbertheory.science.unimelb.edu.au">Number Theory Group</a> at the University of Melbourne, and president of <a href="https://sites.google.com/view/ntdu/home">Number Theory Down Under</a>.
</p>
<p>
<a href="https://people.mpim-bonn.mpg.de/medved/">Anna Medvedovsky</a>
and I taught a short course on Galois representations and modular forms at the
<a href="https://conferences.cirm-math.fr/2801.html">Introduction to SAGA research school</a>
at Luminy in early 2023.
</p>
<p><a href="https://cywu.github.io/">Chenyan Wu</a> and I organised the <a href="https://numbertheory.science.unimelb.edu.au/2020/07/05/ntdu-8/">2020 Number Theory Down Under meeting</a>.</p>
<h2>Recent publications (<a href="publications.html">more</a>)</h2>
<ul>
<li>A. Ghitza, D. Gupta, M. Kortge, <a href="https://arxiv.org/abs/2604.11330">The solvability of the inverse volcano problem over non-prime finite fields</a>, preprint (April 2026), 33 pages.</li>
<li>
A. Ghitza,
<a href="https://sites.google.com/site/takuyayamauchigsp4/webpage-of-takuya-yamauchi">T. Yamauchi</a>: <a href="https://arxiv.org/abs/2509.00635">The non-existence of some Galois representations of moderate degree in small characteristic</a>, preprint (August 2025), 20 pages.
</li>
<li>
A. Ghitza,
<a href="https://sites.google.com/site/takuyayamauchigsp4/webpage-of-takuya-yamauchi">T. Yamauchi</a>: <a href="https://doi.org/10.5802/jtnb.1291">Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields</a>,
<a href="https://jtnb.math.u-bordeaux.fr/">Journal de Théorie des Nombres de Bordeaux</a>
<a href="https://jtnb.centre-mersenne.org/issues/JTNB_2024__36_2/">36, no. 2</a>
(2024), 637-660.
</li>
<li>
<a href="https://sites.google.com/view/samuele-anni/home">S. Anni</a>, A. Ghitza, <a href="https://people.mpim-bonn.mpg.de/medved/">A. Medvedovsky</a>: <a href="https://doi.org/10.5281/zenodo.11221647">Elementary symmetric functions and deep power-sum congruences</a>,
<a href="https://math.colgate.edu/~integers/">Integers</a>
<a href="https://math.colgate.edu/~integers/vol24.html">24</a>
(2024),
<a href="https://math.colgate.edu/~integers/y46/y46.pdf">Paper No. A46</a>, 26 pp.
</li>
<li>
A. Ghitza:
<a href="https://hdl.handle.net/2433/265150">Effective computation of Kurihara numbers</a>, Appendix to
<a href="https://hdl.handle.net/2433/265150">Indivisibility of Kato's Euler systems and Kurihara numbers</a>
by <a href="https://caya.byus.net/">Chan-Ho Kim</a>, in
<a href="https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/265127">Proceedings</a>
of the workshop
<a href="https://sites.google.com/view/rims-ant2018/english">Algebraic Number Theory and Related Topics 2018</a>,
<a href="https://www.kurims.kyoto-u.ac.jp/en/index.html">RIMS</a>
<a href="https://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu.html">Kôkûyroku Bessatsu</a>
<a href="https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/265127">B86</a>
(2021), 63-86.
</li>
<li>
<a href="https://www.elleneischen.com/">E. Eischen</a>, <a href="https://www.linkedin.com/in/max-flander/">M. Flander</a>, A. Ghitza, <a href="https://www.its.caltech.edu/~mantovan/">E. Mantovan</a>, <a href="https://sites.google.com/view/angusmca">A. McAndrew</a>: <a href="https://doi.org/10.2140/ant.2021.15.1469">Differential operators mod p: analytic continuation and consequences</a>,
<a href="https://msp.org/ant/">Algebra and Number Theory</a>
<a href="https://msp.org/ant/2021/15-6/index.xhtml">15, no. 6</a>
(2021), 1469-1504.
</li>
<li>
<a href="https://math.uchicago.edu/~fcale/">F. Calegari</a>, <a href="https://math.mit.edu/~shivac/">S. Chidambaram</a>, A. Ghitza: <a href="https://doi.org/10.1090/mcom/3434">Some modular abelian surfaces</a>,
<a href="https://www.ams.org/publications/journals/journalsframework/mcom">Mathematics of Computation</a>
<a href="https://www.ams.org/journals/mcom/2020-89-321/home.html?active=allissues">89, no. 321</a>
(2020), 387-394.
</li>
</ul>
<h2>Current teaching (<a href="teaching.html">more</a>)</h2>
<ul>
<li>
<a href="teaching/2026ntc.html">2026S2 MAST30035 Number Theory and Cryptography</a>
</li>
</ul>
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